1 Department of Business Administration SPRING 200 7 -0 8 Management Science by Asst. Prof. Sami...

1

Department of Business Administration

SPRING 2007-08Management Science

byby

Asst. Prof. Sami FethiAsst. Prof. Sami Fethi

© 2007 Pearson Education

2© 2007/08, Sami Fethi, EMU, All Right Reserved. Operations Research

Ch 6: Transportation and Assignment

Chapter TopicsChapter Topics

The Transportation Model

Solution of a Transportation Problem

The Assignment Model

Solution of an Assignment Problem


Ch 6: Transportation and AssignmentOverview

Part of a larger class of linear programming problems known as network flow models.

Possess special mathematical features that enabled development of very efficient, unique solution methods.

Methods are variations of traditional simplex procedure.

Detailed description of methods is contained in CD-ROM Module B, Transportation and Assignment Solution Methods.

Text focuses on model formulation and solution with Excel and QM for windows.


Ch 6: Transportation and AssignmentThe Transportation Model

Characteristics

A product is transported from a number of sources to a number of destinations at the minimum possible cost.

Each source is able to supply a fixed number of units of the product, and each destination has a fixed demand for the product.

The linear programming model has constraints for supply at each source and demand at each destination.

All constraints are equalities in a balanced transportation model where supply equals demand.

Constraints contain inequalities in unbalanced models where supply does not equal demand.


Ch 6: Transportation and AssignmentThe Transportation Model

Characteristics

Transportation modelling is an iterative procedure for solving problems that involve minimizing the cost of shipping products from a series of sources to a series of destinations.

Origin Points (or sources) can be factories, warehouses, car rental agencies like AVIS or any other points from which goods are shipped.

Destinations are any points that receive goods.

Transportation models are useful when considering alternative facility locations. The choice of a new location depends on which will yield the minimum cost for the entire system


Ch 6: Transportation and AssignmentThe Transportation

Model Characteristics

To use the transportation model we need to know the following:

The origin points and the capacity or supply per period at each The destination points and the demand per period at each The cost of shipping one unit from each origin to each

destination The transportation problem can be regarded as a generalization of the

assignment problem. In an assignment problem we have a number of origins each processing one item, and the same number of destinations each requiring one item and are asked to empty the origins and fill the destinations in such a way the Total Effectiveness is optimized. In a transportation problem we have “m” origins, with origin “i” processing “ai” items and “n” destinations (possibly different number from “m”) with destination “j” requiring “bj” items, and with

ai = bj.



We are given the m.n costs associated with shipping one item from any origin to any destination, and are asked to empty the origins and fill the destinations in such a way that the total cost is minimized.

The assignment problem is seen to be a special case of transportation problem in which m = n, all the ai and bj are unity.

The iterative routine to be presented as the mode of the solution of the transportation problem involves a succession of “feasible solutions” of gradually diminishing cost; eventually the minimum achievable cost is reached, and the corresponding feasible solution is optimal.

The Transportation Model Characteristics



Transportation Model Example1 (1)



Transportation Model Example (2 )



Transportation Model Example (3)


Ch 6: Transportation and AssignmentTransportation Model Example

(4)


Ch 6: Transportation and AssignmentTransportation Model Example

(5)



Transportation Model Example 2(1)



Transportation Model Example(2)



Transportation Model Example(4)



Special form of linear programming model similar to the transportation model.

Supply at each source and demand at each destination limited to one unit.

In a balanced model supply equals demand.

In an unbalanced model supply does not equal demand.

The Assignment ModelCharacteristics



The Assignment ModelCharacteristics



Assignment Model Example 1(1)



Assignment Model Example(2)



Assignment Model Example (3)



Assignment Model Example (4)


Ch 6: Transportation and AssignmentAssignment Model Example 5

(1)



Assignment Model Example 5 (2)



(1) (minimize)



Assignment Model Example 6 (2) (minimize)



(3) (minimize)



(4) (minimize)



End of chapter

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